Hello, please show me the way how you get the answer of this question this is fi
ID: 3361269 • Letter: H
Question
Hello, please show me the way how you get the answer of this question
this is finance ( insurance) question please show me how you calculat the answer because I don't know how. please send me the answer as soon as posible.
Here is the question
2) Find single net premium for a $1000 life annuity for a 97 year old. Assume : Interest rat = 10%; Annuity paid at the end of each year. Assume: everyone dies by age 100 and the mortality table used is as following
Age
Number of survivor
97
6050
98
3145
99
1076
100
0
Hint:
year
Probability of a 97- year- old surviving
Expected payment $1000 * prob
PV of expected payment
1
2
3
Age
Number of survivor
97
6050
98
3145
99
1076
100
0
Explanation / Answer
Solution
Let nqx be the probability of death of a person aged x to x+n age
Probability of survival = 1- nqx
Probability of survival = number of lives at age x + 1 / number of lives at age x
p97 = 3145/6050 = 0.51983
2p97 = 1076/6050 = 0.17785
3p97 = 0/6050 = 0
Net premium = 1000*0.51983*(1+i)-1 + 1000*0.17785*(1+i)-2 + 0 where, i = 10%
= 619.56
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